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We introduce a stochastic integral with respect to cylindrical Lévy processes with finite p -th weak moment for $$p\in [1,2]$$ p ∈ [ 1 , 2 ] . The space of integrands consists of p -summing operators between Banach spaces of martingale type p . We apply the developed integration theory to establish the existence of a solution for a stochastic evolution equation driven by a cylindrical Lévy process.

Stochastic Integration with Respect to Cylindrical Lévy Processes by p-Summing Operators